Abstract
For a class of finite shift planes introduced by Coulter and Matthews, we give a set of representatives for the isomorphism types, determine all automorphisms and describe all polarities explicitly. The planes in question are the only known examples of finite shift planes that are not translation planes. Each non-desarguesian Coulter–Matthews plane admits precisely two conjugacy classes of orthogonal polarities. In addition, each Coulter–Matthews plane of square order admits exactly one conjugacy class of unitary polarities. We prove that most of the corresponding unitals are not classical.
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Communicated by J.D. Key.
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Knarr, N., Stroppel, M. Polarities and unitals in the Coulter–Matthews planes. Des. Codes Cryptogr. 55, 9–18 (2010). https://doi.org/10.1007/s10623-009-9326-7
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DOI: https://doi.org/10.1007/s10623-009-9326-7